It has been known, as disclosed for example in U.S. Pat. No. 4,345,431 and Japanese Patent Public Disclosure No. 49-71315 to provide an exhaust gas cleaning device having filter means in the exhaust gas passage of a diesel engine to trap particulate materials in the exhaust gas, thereby to prevent particulates from being discharged with the exhaust gas. Such filter means is provided with burner means upstream the filter means to have carbon particles on the filter burnt, thereby to prevent clogging of the filter. The filter means includes a filter element which is of a cylindrical configuration and arranged so that the exhaust gas is passed through the filter element radially inwardly or outwardly. In this type of arrangement, the burner is located adjacent to one axial end of the filter element so that the flame from the burner is applied in a parallel direction to the cylindrical inner or outer surface of the element where the exhaust gas enters the filter element. It should, however, be noted that the arrangement is disadvantageous in that the burner flame cannot be applied uniformly on the filter surface where carbon particles are apt to be deposited so that carbon deposits cannot satisfactorily be removed. Moreover, there is a risk that the filter element is locally overheated by the burner flame to the extent that the life of the burner is shortened. It should further be noted that, in the above-mentioned type of exhaust gas cleaning devices, the arrangement is such that the flame from the burner is mixed with the exhaust gas before the combustion is completed so that burner fuel is not completely burnt before it reaches the filter element. As a result, an increased amount of fuel is required for preventing clogging of the filter, causing poor fuel economy of the engine. On the other hand, in order to obtain complete combustion of the burner fuel, it is required to increase the length of the burner, producing a problem of providing increased space for the burner.